Understanding the concepts on Degrees of Freedom

QUESTION 1 : A five storey structure with 5 translational DOF is shown here. Each storey has mass ‘m’. The eigenvalue problem has been solved and the 5 periods of vibration T_n and their corresponding mode shapes, φ_n has been derived.

The fundamental period of vibration and its associated mode shape as below :

(T₁ = 2 seconds) (T₂ = 0.6852 seconds) (T₃ = 0.4346 seconds) (T₄ = 0.3383 seconds) (T5 = 0.2966 seconds)

AIM :

To calculate Ln,Mn and Γn for each of the five modes

To calculate the effective modal mass Mn* and the modal mass participating ratio for the 5 modes.

To find the base shear for each of the 5 modes of vibration and the combined base shear as per the SRSS rule.

SOLUTION :